Blendshape and skeletal animation

I have very simple animation playing on my character:

https://forums.unrealengine.com/attachment.php?attachmentid=120012&d=1480798259

Now it is all fine, until I apply blendshape, which makes my character - for example - larger.

Then I get something like this:

https://forums.unrealengine.com/attachment.php?attachmentid=120013&d=1480798339

As you can see, hands are very oddly stretched. Its like skinning information is not consistent with new blend shape vertex position. Any idea, how to handle that?